We critically reconsider the Landau-Ginzburg-Wilson (LGW) approach to critical phenomena in the presence of gauge symmetries. In the LGW framework, to obtain the universal features of a continuous transition, one identifies the order parameter Φ and considers the corresponding most general Φ 4 field theory that has the same symmetries as the original model. In the presence of gauge symmetries, one usually considers a gauge-invariant order parameter and a LGW field theory that is invariant under the global symmetries of the original model. We show that this approach, in which the gauge dynamics is effectively integrated out, may sometimes lead to erroneous conclusions on the nature of the critical behavior. As an explicit example, we show that the above-described LGW approach generally fails for the three-dimensional ferromagnetic and antiferromagnetic CP N−1 models, which are invariant under global U(N ) and local U(1) transformations. We point out possible implications for the finite-temperature chiral transition of nuclear matter.

We investigate the critical properties of the three-dimensional antiferromagnetic RP^{N-1} model, which is characterized by a global O(N) symmetry and a discrete Z_{2} gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general Φ^{4} theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_{2} gauge symmetry.

The correlations detected by the mutual information in the propensities of a molecular viscous liquid are studied by molecular-dynamics simulations. Dynamic heterogeneity is evidenced and two particle fractions with different mobility and relaxation identified. The two fractions exhibit scaling of their relaxation in terms of the rattling amplitude of the particle trapped in the cage of the first neighbours u 2 . The scaling master curve does not differ from the one found for bulk systems, thus confirming identical results previously reported in other systems with strong dynamic heterogeneity as thin molecular films. Excitation of planar and globular structures at short and long times with respect to structural relaxation, respectively, is revealed. Some of the globular structures are different from the ones evidenced in atomic mixtures. States with equal u 2 are found to have identical time dependence of several quantities, referring to both bulk and the two fractions with heterogeneous dynamics, at least up to the structural relaxation time τα.